The Re-Granulation on Topological Structure of Granular Computing

Granular computing is an important research hotspot in artificial intelligence field. As one of the most important granular computing models, the quotient space theory mainly focuses on converting the fine granularity (original topological space) into the coarse granularity (quotient space). However, the granulation is an information decreasing and irreversible process which cannot be recovered losslessly from quotient space to original space. Therefore, this paper focuses on study the regranulation on topological structure of granular computing: Firstly, it defines concept of re-granulation which provides a mathematical method for reversibly transforming coarse granularity to fine one; Secondly, by theorems and examples it presents two reversible conditions of re-granulation --- defining a bijective mapping or keeping every open-set being saturated set on original space, which guarantee the information unchanging while restoring the problem from quotient space to original space. This paper has provided a formal computing framework for the reversibility of granularity on topological structure of granular computing.